Over 99

$\begin{matrix} a & \equiv & { 100 }^{ 9999 } & \\ & \equiv & { 10 }^{ 19998 } & \\ & \equiv & { 10 }^{ 2 }\cdot { \left( 10000 \right) }^{ 4999 } & \\ & \equiv & 100 & \left( \bmod \text{ 9999} \right) \end{matrix}$

Since $0 \leq a < 9999$ , $a = 100$ .